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GCSEMathsEdexcelHigherFlashcards2. AlgebraCoordinate Geometry

Coordinate Geometry (Edexcel GCSE Maths)

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  • FrontCoordinates

    True or False?

    On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

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  • True or False?

    On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

    True.

    On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

  • Which coordinates would be a units left and b units down from the point open parentheses x comma space y close parentheses?

    The coordinates a units left and b units down from the point open parentheses x comma space y close parentheses would be open parentheses x minus a comma space y minus b close parentheses.

  • State an expression for the coordinates of the midpoint between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses.

    The midpoint between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is given by the expression open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses.

  • True or False?

    The x-coordinate of the midpoint is equal to the mean of the x-coordinates of the two points.

    True.

    The x-coordinate of the midpoint is equal to the mean of the x-coordinates of the two points.

    The y-coordinate of the midpoint is also equal to the mean of the y-coordinates of the two points.

  • What does the gradient of a line measure?

    The gradient of a line measures the steepness of the line.

  • True or False?

    A line with a gradient of -4 is steeper than a line with a gradient of -5.

    False.

    A line with a gradient of -5 is steeper than a line with a gradient of -4. The steeper line is the one with the bigger gradient value when you ignore negative signs.

  • True or False?

    The gradient of a line is equal to fraction numerator change space in space y over denominator change space in space x end fraction.

    True.

    The gradient of a line is equal to fraction numerator change space in space y over denominator change space in space x end fraction.

  • State the formula for the gradient of the line that passes through open parentheses x subscript 1 comma y subscript 1 close parentheses and open parentheses x subscript 2 comma y subscript 2 close parentheses.

    The formula for the gradient of the line that passes through open parentheses x subscript 1 comma y subscript 1 close parentheses and open parentheses x subscript 2 comma y subscript 2 close parentheses is m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction.

    The formula m equals fraction numerator y subscript 1 minus y subscript 2 over denominator x subscript 1 minus x subscript 2 end fraction will also give the gradient.

  • True or False?

    A positive gradient means the line goes upwards from bottom left to top right.

    True.

    A positive gradient means the line goes upwards from bottom left to top right.

  • True or False?

    The gradient of the line which passes through open parentheses 4 comma space 5 close parentheses and open parentheses 1 comma space 2 close parentheses can be found by calculating fraction numerator 2 minus 5 over denominator 4 minus 1 end fraction.

    False.

    The gradient of the line which passes through open parentheses 4 comma space 5 close parentheses and open parentheses 1 comma space 2 close parentheses can not be found by calculating fraction numerator 2 minus 5 over denominator 4 minus 1 end fraction.

    The order needs to be consistent. If the second coordinate is used first for the y coordinates, then the second coordinate should be used first for the x coordinates.

    It should be either fraction numerator 2 minus 5 over denominator 1 minus 4 end fraction or fraction numerator 5 minus 2 over denominator 4 minus 1 end fraction.

  • State the formula for the length of the line segment between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses.

    The formula for the length of the line segment between open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root.

    This is just using Pythagoras' theorem on the line segment between the two points.

  • True or False?

    The length of the line segment between open parentheses 4 comma space minus 1 close parentheses and open parentheses 7 comma space 6 close parentheses can be found by calculating square root of open parentheses 4 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 7 minus 6 close parentheses squared end root.

    False.

    The length of the line segment between open parentheses 4 comma space minus 1 close parentheses and open parentheses 7 comma space 6 close parentheses can not be found by calculating square root of open parentheses 4 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 7 minus 6 close parentheses squared end root. Each bracket should be the difference between the x values or the y values.

    It should be square root of open parentheses 7 minus 4 close parentheses squared plus open parentheses 6 minus open parentheses negative 1 close parentheses close parentheses squared end root.

Previous:FunctionsNext:Linear Graphs

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation